Turbomachinery is used in many applications to perform work on or extract work from both gaseous and liquid fluids. Examples of such machinery includes gas turbines, axial and centrifugal fans, marine and aviation propellers, fan blades, helicopter blades and tail rotors, wind turbines, and steam and hydraulic power turbines. This machinery, by design, may contain one or more of a broad class of rotating and fixed appendages including blades, vanes, foils, and impellers depending on the needs of the particular machine. These appendages are beam-like structures, often cantilevered, and have natural frequencies of vibrations, or resonant frequencies, that are excited by mechanical vibration and fluid flow. In all turbomachinery, power is transmitted via shafts of one form or another.
Rotating appendages such as gas turbine blades are prone to vibration at critical speeds, which leads to fatigue and eventually pre-mature, and often catastrophic, failure of the component. Ensembles of such blades are components of turbines used as prime movers, such as gas turbines, as well as power generators, such as hydraulic turbines. Vibration of the turbine blades is caused by a combination of dynamic effects including imbalance of the rotating system and torsional vibration of the power transmission shaft, and fluid dynamic forcing. In certain operating conditions these phenomenon conspire to excite the natural modes of vibration in the turbine blades, and if left unchecked drive the system to failure. Natural frequencies are defined as those frequencies at which an ideal, lossless system will vibrate with zero input excitation power. In real systems, which always have a certain amount of intrinsic or added damping, the system will respond at the natural frequencies and displacement amplitude will grow to the point that damping (i.e., conversion of mechanical energy to heat) dominates or until the part fails.
Fixed appendages such as stator vanes in a gas turbine, as an example, are also subject to dynamic loading, due in part, to the fluid flow dynamics and due, in part, to coupled vibrations from other parts of the turbomachine. Like their rotating counterpart, these fixed appendages have resonant frequencies, which can be excited by system dynamics. While the fixed appendages do not have the extra load imposed by centrifugal forces, as do the rotating appendages, excitation of the components at their resonant frequency can still lead to excessive dynamic loads and thence to premature failure.
In all turbomachinery, there are one or more power transmission shafts to-which the rotating components are attached directly or indirectly. As with the other components, the transmission shafts also have resonant frequencies, which are a function of the shaft geometry, the loading imposed by the rotating appendages, and the boundary conditions imposed by the locations of the bearings holding the shaft system in place. At critical speeds, rotating shafts become dynamically unstable with large lateral amplitudes. Resonance in the shaft, as with the other components, is to be minimized so as to minimize wear on bearings, minimize cyclical fatigue of the shaft, and thus to increase the service life and reliability of the equipment.
Of the three vibrating components of turbomachinery, the rotating appendages are under the most stress and are the most difficult to treat due, in large part, to the combined effects of mechanical and fluid dynamics, the latter of which is associated with fluid turbulence. Fluid effects on rotating appendages apply as well to the fixed appendages, which are strongly affected by fluid dynamic excitation. Vibrations in shafts are only slightly affected by fluid dynamics, but complicated mechanical dynamics cause significant loads in some cases with large vibration induced motion.
While mechanical and fluid dynamic loading both result in excitation of the cantilever modes of vibration of turbine blades, their causative mechanisms are quite different. Mechanical imbalance of an ideal infinitesimally thin rotor disk, or radial array of turbine blades, only produces a radial force on each blade, and cannot, in principle, excite the bending cantilever motion that results in blade fatigue. In real systems, however, two factors contribute to the excitation of bending modes in the blades. The first is two-plane rotor imbalance, which imparts a moment at the base of the blade where it connects to the hub. The second is imperfections in the radial alignment of the turbine blade, which permits purely radial motions of the hub to excite bending motions of the blade. Two-plane rotor imbalance tends to excite bending motion in a plane parallel to the axis of the power transmission shaft and perpendicular to the plane of the turbine blade disc assembly. Misalignment of the turbine blade tends to convert radial motion of the hub into bending motion in both planes, i.e., that plane parallel to the transmission shaft and that plane parallel to the turbine blade disc assembly.
Further dynamic forcing on the blades results from torsional vibrations of the transmission shaft. These vibrations are associated with the natural torsional modes of the shaft assembly and are excited by any transient event such as changes in speed. Torsional vibration in the shaft couples to bending vibration in the turbine blades with motion primarily in the plane parallel to the turbine blade disc assembly.
The distinction between the two planes of bending motion is not clearly defined. Specifically, asymmetry of the blade shape with respect to the plane of rotation causes the two bending directions to be coupled. As a result, any attempt to minimize bending motion must be effective in both planes. The important bending plane, in fact, is that plane which runs the length of the blade and cuts through its narrowest dimension.
Fluid dynamic loading is a result of vortex shedding at the trailing edge of the (rotating or fixed) blade. Vortex shedding frequencies vary from section to section along the length of the blade due to slight variations in the blade structure and variations of the flow velocity across the blade. The range of vortex shedding frequencies for any given blade can thus span a relatively broad bandwidth. If one or more natural frequencies of the blade lie within the band of vortex shedding frequencies, then the blade will be excited into motion. In ship propellers this phenomenon is known as singing propellers. It has been found that blades with relatively straight trailing edges, as is the case for many turbine blades, are more prone to singing than those with curved trailing edges. Singing continues to excite the blade until intrinsic or added damping limits the buildup of displacement amplitude.
Previous treatments for vibration in turbomachinery appendages have focused on applying damping materials or mechanisms at point locations. The intent is to limit the maximum displacement of the component by converting the dynamic (kinetic) energy of the appendage into heat, which is innocuous in terms of the performance and service life of the machine. Placing damping treatments at localized points is effective if there exist large resonant system dynamics at the chosen point, which is not always true.
For blades and stator vanes, previous damping treatments have most often been applied at the base of the appendages, where they attach to the rest of the machine, at the tip in the form of a shroud for the blades, and at the inner and outer shroud for vanes. Damping at the base is attractive because the primary modification to the blade or vane is in the attachment configuration and does not affect the functional shape of the foil. In addition, for rotating blades, the extra weight associated with the damping treatment is subjected to reduced centrifugal forces because of its proximity to the axis of rotation. Damping at the blade tip by a shroud is effective in reducing the dynamic vibration levels of cantilevered blades, but comes at the cost of increased weight and centrifugal forces imposed on the blades and the rotor hub. Intermediate damping positions have been used in the form of snubbers that are positioned between the blades at locations part way between the blade root and tip. While effective in damping the resonant vibrations, especially if used with a shroud, the snubbers impose extra weight, and in addition, disturb the fluid flow around the appendage, which reduces the efficiency of the machine.
High temperature gas turbines are especially difficult to treat. In such situations complications beyond the high centrifugal force exist. Specifically, the design must deal with heat combined with the fact that low order modes of vibration are notoriously difficult to treat using passive damping methods. The temperature of operation in gas turbine engines, for example, is in the vicinity of 1300.degree. F., which renders useless any conventional viscoelastic polymer or resin. Previous attempts have been made to add ceramic damping layers to the external surfaces of turbine blades, but the combination of heat and high centrifugal force renders the treatment short lived.
Other previous treatments are based on friction devices mounted at the connections between the blade and the hub. The friction devices rely on the relative motion between the blade base and the hub. With a frictional surface mounted at this location, vibrational energy is extracted from the blade and converted to heat. The shortcoming in this approach is that the motion of the blade is low at the junction between the blade and the hub. Effective passive damping is only achieved when treatments are placed at locations of large displacement.
In another approach, dynamic absorbers have been used to reduce vibration levels in many types of devices. A liquid has been placed within a chamber of a hollow blade. The liquid oscillates within the chamber, which is sized to produce a resonant frequency approximately the same as that of a dominant resonance in the blade. The combination of the blade resonance and the fluid resonance form, in a simplified analogy, a two degree-of-freedom system in which energy from the blade, which has low intrinsic damping is coupled to energy in the liquid, which through proper selection of viscosity, has high intrinsic damping. The deficiency of this approach is that the dynamic absorber formed by the liquid oscillator only extracts energy from the blade in a relatively narrow band of frequencies. Since the excitation mechanism is broadband (a combination of fluid dynamic vortex shedding and mechanical vibrations with many harmonics) then a narrowband absorber will only provide partial relief. Dynamic absorbers have also been used for damping shafts.
In still another previous approach, treatment of vibrations associated with power transmission shafts and structural acoustics have included high-density granular fill such as sand or lead shot. Broadband treatment has been achieved by filling hollow shafts with sand, but the enhanced performance comes at the cost of a substantial weight increase that is unsuitable for many applications.